\magnification=1440
\font\bigtenrm=cmr10 scaled\magstep4
Abstract for Gary Gordon, A $\beta$ Invariant for Greedoids and Antimatroids

We extend Crapo's $\beta $ invariant from matroids to greedoids, concentrating
especially on antimatroids.  Several familiar expansions for $\beta (G)$ have greedoid analogs. 
We give combinatorial interpretations for $\beta (G)$ for simplicial shelling antimatroids
associated with chordal graphs.  When $G$ is this antimatroid and $b(G)$ is the number of blocks
of the chordal graph $G$, we prove $\beta (G)=1-b(G)$.


\bye